SOLUTION: If the larger of the two numbers is divided by the smaller,the quotient and the reminder are 2 each.If 5 times the smaller number is divided by the larger,the quotient and the remi

Algebra ->  Linear-equations -> SOLUTION: If the larger of the two numbers is divided by the smaller,the quotient and the reminder are 2 each.If 5 times the smaller number is divided by the larger,the quotient and the remi      Log On


   

Question 940677: If the larger of the two numbers is divided by the smaller,the quotient and the reminder are 2 each.If 5 times the smaller number is divided by the larger,the quotient and the reminder are still 2 each.Find the two numbers.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
let the larger number be x.
let the smaller number be y.

you get:

larger number divided by smaller number = 2 + remainder of 2 becomes:

x/y = 2 + 2/y

5 times smaller number divided by larger number= 2 + remainder of 2 becomes:

5y/x = 2 + 2/x

solve for x in the equation of x/y = 2 + 2/y to get:

x = 2y + 2

replace x with 2y + 2 in the equation of 5y/x = 2 + 2/x to get:

5y/(2y + 2) = 2 / (2y + 2)

solve for y in this equation to get:

y = 6

replace y with 6 in the equation of x/y = 2 + 2/y to get:

x = 14

14/6 = 2 + remainder of 2.

5 * 6 = 30 / 14 = 2 + remainder of 2.

the solution is correct.